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138 changes: 138 additions & 0 deletions
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functions/function_usage_examples/arithmetic/modular_exp/modular_exp_example.ipynb
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|---|---|---|
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "f6834a62-d124-48f6-bd87-d313b7eb5054", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Modular Exponentiation\n", | ||
| "\n", | ||
| "The `modular_exp` function raises a classical integer `a` to the power of a quantum number `power` modulo classical integer `n`, times a quantum number `x`.\n", | ||
| "\n", | ||
| "The function performs:\n", | ||
| "$$|x\\rangle |power\\rangle = |(a^{power} \\mod n)\\cdot x\\rangle | power\\rangle$$\n", | ||
| "\n", | ||
| "Specifically if at the input $x=1$, at the output $x=a^{power} \\mod n$." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "b54ad820-bdd9-4fbe-bbe7-a7d6a3db046b", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Example\n", | ||
| "\n", | ||
| "This example generates a quantum program that initializes a `power` variable with a uniform superposition, and exponentiate the classical value `A` with `power` as the exponent, in superposition. The result is calculated inplace to the variable `x` module `N`.\n", | ||
| "\n", | ||
| "Notice that `x` should have size of at least $\\lceil(log_2(N) \\rceil$, so it is first allocated with a fixed size, then initialized with the value '1'." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 39, | ||
| "id": "6fca39ac-e769-4d85-b9a9-0bed93d2b775", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "\n", | ||
| "from classiq import *\n", | ||
| "from classiq.qmod.symbolic import ceiling, log\n", | ||
| "\n", | ||
| "# constants\n", | ||
| "N = 5\n", | ||
| "A = 4\n", | ||
| "\n", | ||
| "\n", | ||
| "@qfunc\n", | ||
| "def main(power: Output[QNum], x: Output[QNum]) -> None:\n", | ||
| " allocate(ceiling(log(N, 2)), x)\n", | ||
| " inplace_prepare_int(1, x)\n", | ||
| "\n", | ||
| " # initialize a uniform superposition of powers\n", | ||
| " allocate(3, power)\n", | ||
| " hadamard_transform(power)\n", | ||
| "\n", | ||
| " modular_exp(n=N, a=A, x=x, power=power)\n", | ||
| "\n", | ||
| "\n", | ||
| "qmod = create_model(main)\n", | ||
| "qmod = create_model(main, out_file=\"modular_exp_example\")\n", | ||
| "qprog = synthesize(qmod)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 40, | ||
| "id": "d7931d74-f1b6-4374-832e-eee4e3e0ab4b", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "[{'power': 3, 'x': 4}: 136,\n", | ||
| " {'power': 1, 'x': 4}: 135,\n", | ||
| " {'power': 7, 'x': 4}: 130,\n", | ||
| " {'power': 5, 'x': 4}: 124,\n", | ||
| " {'power': 2, 'x': 1}: 124,\n", | ||
| " {'power': 4, 'x': 1}: 123,\n", | ||
| " {'power': 6, 'x': 1}: 117,\n", | ||
| " {'power': 0, 'x': 1}: 111]" | ||
| ] | ||
| }, | ||
| "execution_count": 40, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "result = execute(qprog).result_value()\n", | ||
| "result.parsed_counts" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "0398be45-a152-4225-ba7b-49c1f37b197d", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Verify all results are as expected:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 41, | ||
| "id": "1363a9ae-567a-4bf1-911d-f17da9d6859c", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "assert np.all(\n", | ||
| " [\n", | ||
| " count.state[\"x\"] == (A ** count.state[\"power\"] % N)\n", | ||
| " for count in result.parsed_counts\n", | ||
| " ]\n", | ||
| ")" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbconvert_exporter": "python", | ||
| "pygments_lexer": "ipython3", | ||
| "version": "3.11.4" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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functions/function_usage_examples/arithmetic/modular_exp/modular_exp_example.metadata.json
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| { | ||
| "friendly_name": "Modular Exponentiation", | ||
| "description": "Modular Exponentiation with an Exponent of Quantum Variable", | ||
| "qmod_type": ["function"], | ||
| "level": ["demos", "basic"] | ||
| } |
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functions/function_usage_examples/arithmetic/modular_exp/modular_exp_example.qmod
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| qfunc main(output power: qnum, output x: qnum) { | ||
| allocate(ceiling(log(5, 2)), x); | ||
| inplace_prepare_int(1, x); | ||
| allocate(3, power); | ||
| hadamard_transform(power); | ||
| modular_exp(5, 4, x, power); | ||
| } |
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...function_usage_examples/arithmetic/modular_exp/modular_exp_example.synthesis_options.json
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| { | ||
| "constraints": { | ||
| "max_width": null, | ||
| "max_depth": null, | ||
| "max_gate_count": {}, | ||
| "optimization_parameter": "no_opt" | ||
| }, | ||
| "preferences": { | ||
| "machine_precision": 8, | ||
| "backend_service_provider": null, | ||
| "backend_name": null, | ||
| "custom_hardware_settings": { | ||
| "basis_gates": [ | ||
| "cx", | ||
| "rz", | ||
| "t", | ||
| "z", | ||
| "u", | ||
| "sx", | ||
| "sxdg", | ||
| "u2", | ||
| "y", | ||
| "x", | ||
| "cy", | ||
| "cz", | ||
| "sdg", | ||
| "p", | ||
| "s", | ||
| "id", | ||
| "ry", | ||
| "rx", | ||
| "r", | ||
| "h", | ||
| "u1", | ||
| "tdg" | ||
| ], | ||
| "connectivity_map": null, | ||
| "is_symmetric_connectivity": true | ||
| }, | ||
| "debug_mode": true, | ||
| "output_format": ["qasm"], | ||
| "pretty_qasm": true, | ||
| "qasm3": null, | ||
| "transpilation_option": "auto optimize", | ||
| "solovay_kitaev_max_iterations": null, | ||
| "timeout_seconds": 300, | ||
| "optimization_timeout_seconds": null, | ||
| "random_seed": 1209628880 | ||
| } | ||
| } |
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| qfunc qft(target: qbit[]) { | ||
| repeat (index: target.len / 2) { | ||
| SWAP(target[index], target[(target.len - 1) - index]); | ||
| } | ||
| qft_no_swap(target); | ||
| } |
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